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Math Help - rhombus diagonal

  1. #1
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    rhombus diagonal

    a rhombus having side 6cm. and altitude 4cm. which diagonals are 6cm and 8cm.is it possible to draw
    this rhombus? by area method if
    one dia is 8cm then
    (1/2*6*4)+(1/2*6*4)=1/2*6*8
    its right but if one dia is 6cm then rhombus will be two equilateral triangl.and another diagonal will paas through mid point of triangle then the length of another diagonal will never be less than 2*root of 27
    therefore i wanna know whether this problem is right or wrong give me clarification
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  2. #2
    Senior Member BAdhi's Avatar
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    if we consider the two adjecsent side and the 6cm diagonal, it forms a equilateral triangle so the other diagonal should be 2(3\sqrt{3}) which is not equal to 8cm so i think this rombus cannot be formed.
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  3. #3
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    Hello, sandeeptiwari674!

    Another approach . . .


    A rhombus having side 6cm, and altitude 4cm, and diagonals are 6cm and 8cm.
    Is it possible to draw this rhombus? . No

    The rhombus is composed of two equilateral triangles.

    Code:
    
                      6
                * - - - - - *
               /:\         /
              / : \       /
            6/  :  \6    /6
            /   :   \   /
           /    :    \ /
          * - - + - - *
                6 

    In an equilateral triangle with side 6,
    . . the altitude is 3\sqrt{3} \,\approx\,5.2 cm.

    The altitude of the rhombus cannot be 4.

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